

A100294


Numbers of the form a^5 + b^4 with a, b > 0.


10



2, 17, 33, 48, 82, 113, 244, 257, 259, 288, 324, 499, 626, 657, 868, 1025, 1040, 1105, 1280, 1297, 1328, 1539, 1649, 2320, 2402, 2433, 2644, 3126, 3141, 3206, 3381, 3425, 3750, 4097, 4128, 4339, 4421, 5120, 5526, 6562, 6593, 6804, 7221, 7585, 7777, 7792
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OFFSET

1,1


COMMENTS

In view of computing A300566, it would be interesting to have an efficient way to check whether a given (large) n is in this sequence.  M. F. Hasler, Apr 25 2018


LINKS

Table of n, a(n) for n=1..46.


MATHEMATICA

lst={}; Do[p=a^5+b^4; If[p<15000, AppendTo[lst, p]], {a, 16}, {b, 32}]; Union[lst]


PROG

(PARI) A100294_vec(L=10^6, k=4, m=5, S=List())={for(a=1, sqrtnint(L1, m), for(b=1, sqrtnint(La^m, k), listput(S, a^m+b^k))); Set(S)} \\ all terms up to limit L.  M. F. Hasler, Apr 25 2018
(PARI) is(n, k=4, m=5)=for(a=1, sqrtnint(n1, m), ispower(na^m, k) && return(a)) \\ Returns a > 0 if n is in the sequence, or 0 otherwise.  M. F. Hasler, Apr 25 2018


CROSSREFS

Cf. A100274 (primes of the form a^5 + b^4).
Subsequence of A100292 (a^5 + b^2); see also A055394 (a^2 + b^3), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100293 (a^5 + b^3), A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6).
Roots of 6th powers are listed in A300566 (z such that z^6 = x^5 + y^4 for some x, y >= 1); see also A300564 (z^4 = x^3 + y^2) and A242183, A300565 (z^5 = x^4 + y^3), A300567 (z^7 = x^6 + y^5), A302174.
Sequence in context: A178145 A055261 A307690 * A192453 A284779 A018529
Adjacent sequences: A100291 A100292 A100293 * A100295 A100296 A100297


KEYWORD

nonn


AUTHOR

T. D. Noe, Nov 18 2004


STATUS

approved



